Question

Consider the function below.
f(x) = (x^2)/(x−9)^2

(a) Find the vertical and horizontal asymptotes. x=? y=?

(b) Find the interval where the function is increasing. (Enter your answer using interval notation.)

Find the interval where the function is decreasing. (Enter your answer using interval notation.)

(c) Find the local minimum value.

(d) Find the inflection point.(x,y)=

Find the interval where the function is concave up. (Enter your answer using interval notation.)

Find the intervals where the function is concave down. (Enter your answer using interval notation.)

Answer 1

a
when x = 9, function is vertical y--->oo
when x is large negative or positive then y = 1
TRY NUMBERS!

b
dy/dx = [2x(x-9)^2 - x^2(2)]/(x-9)^4

= [2x^3 -38x^2 + 162 x]/(x-9)^2
the bottom is always +
so the top is the whole thing
if + then slope up, if - then slope down
turns out top is divisible by (x-9) so easier than it looks
Find zeros
oh well, use algorithm
http://www.wolframalpha.com/input/?i=x^2%2F%28x-9%29^2

Answer 2

I don't really think of a function as my gf, sorry. I can't consider them-